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TEKS Focus: (6)(B) Prove two triangles are congruent by applying the Side-Angle-Side, AngleSide-Angle, Side-Side-Side, AngleAngle-Side, and Hypotenuse-Leg congruence conditions. (1)(G) Display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication. Geometric figures are congruent if they are the same size and shape. Corresponding angles and corresponding sides are in the same position in polygons with an equal number of sides. Two polygons are congruent polygons if and only if their corresponding sides are congruent. Thus triangles that are the same size and shape are congruent. CPCTC is an abbreviation for the phrase “Corresponding Parts of Congruent Triangles are Congruent.” It can be used as a justification in a proof after you have proven two triangles congruent. To name a polygon, write the vertices in consecutive order. For example, you can name polygon PQRS as QRSP or SRQP, but not as PRQS. In a congruence statement, the order of the vertices indicates the corresponding parts. P Q S R Some hikers come to a river in the woods. They want to cross the river but decide to find out how wide it is first. So they set up congruent right triangles. The figure shows the river and the triangles. Find the width of the river, GH. Explain. 5 meters, by using CPCTC Example: 2 Use the diagram to prove the following. STATEMENT REASON 1. BA DA 1. Given 2. CAB EAD 2. Vertical Angle Theorem 3. CA EA 3. Given 4. BAC DAE 4. SAS 5. C E 5. CPCTC Example 3: STATEMENT REASON 1. AB AC 1. Given 2. M is the midpoint of BC 2. Given 2. BM MC 2. Definition of Midpoint 3. AM AM 3. Reflexive Prop. of Congruence 4. AMB AMC 4. SSS 5. AMB AMC 5. CPCTC Example 4: STATEMENT REASON 1. KN and LM bisect each other 1. Given 2. KH HN and LH HM 2. Definition of Segment Bisector 3. KHL NHM 3. Vertical Angle Theorem 4. KHL NHM 4. SAS 5. KLH NMH 5. CPCTC 6. KL || MN 6. Converse of Alternate Interior Angles Theorem